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Mat. Zametki, 2001, Volume 69, Issue 6, Pages 919–924 (Mi mz706)  

This article is cited in 4 scientific papers (total in 4 papers)

On the Problem of Describing Sequences of Best Trigonometric Rational Approximations

A. P. Starovoitov

Francisk Skorina Gomel State University

Abstract: For a strictly decreasing sequence $\{a_n\}^\infty_{n=0}$ of nonnegative real numbers converging to zero, we construct a continuous $2\pi$-periodic function $f$ such that $R^T_n(f)=a_n$, $n=0,1,2,…$, where $R^T_n(f)$ are best approximations of the function $f$ in uniform norm by trigonometric rational functions of degree at most $n$.

DOI: https://doi.org/10.4213/mzm706

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English version:
Mathematical Notes, 2001, 69:6, 839–844

Bibliographic databases:

UDC: 517.51+517.53
Received: 03.04.2000

Citation: A. P. Starovoitov, “On the Problem of Describing Sequences of Best Trigonometric Rational Approximations”, Mat. Zametki, 69:6 (2001), 919–924; Math. Notes, 69:6 (2001), 839–844

Citation in format AMSBIB
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\paper On the Problem of Describing Sequences of Best Trigonometric Rational Approximations
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\pages 919--924
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1861555}
\zmath{https://zbmath.org/?q=an:0995.41005}
\transl
\jour Math. Notes
\yr 2001
\vol 69
\issue 6
\pages 839--844
\crossref{https://doi.org/10.1023/A:1010242801551}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000169913100025}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. P. Starovoitov, “Remark on a Problem of Rational Approximation”, Math. Notes, 74:3 (2003), 422–424  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. A. P. Starovoitov, “Existence of Continuous Functions with a Given Order of Decrease of Least Deviations from Rational Approximations”, Math. Notes, 74:5 (2003), 701–707  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. Maria Almira J., “On Strict Inclusion Relations Between Approximation and Interpolation Spaces”, Banach J. Math. Anal., 5:2 (2011), 93–105  crossref  mathscinet  zmath  isi  scopus  scopus
    4. Almira J.M. Oikhberg T., “Approximation Schemes Satisfying Shapiro's Theorem”, J. Approx. Theory, 164:5 (2012), 534–571  crossref  mathscinet  zmath  isi  elib  scopus  scopus
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